David explains what beat frequency means, how to find it, and solves a sample problem involving beat frequency. Created by David SantoPietro.

When you spin it around, this toy sounds like a swarm of buzzing bees.

In this optics activity, learners discover that when they rotate a special black and white pattern called a Benham's Disk, it produces the illusion of colored rings. Learners experiment with the speed of rotation and direction of rotation to observe varying patterns. Use this activity to explain to learners how our eyes detect color and how different color receptors in the eye respond at different rates.

Demonstrate the Bernoulli Principle using simple materials on a small or large scale. This resource includes two activities that allow learners to experience the Bernoulli Principle, in which an object is suspended in air by blowing down on it. Use this activity to explain how atomizers work and why windows are sometimes sucked out of their frames as two trains rush past each other.

Bernoulli's principle relates the pressure of a fluid to its elevation and its speed. Bernoulli's equation can be used to approximate these parameters in water, air or any fluid that has very low viscosity. Students learn about the relationships between the components of the Bernoulli equation through real-life engineering examples and practice problems.

This is the first of two videos where Sal derives Bernoulli's equation. Created by Sal Khan.

This is the second of two videos where Sal derives Bernoulli's equation. In the second half of the video Sal also begins an example problem where liquid exits a hole in a container. Created by Sal Khan.

In this activity, a spinning bicycle wheel resists efforts to tilt it and point the axle in a new direction. Learners use the bicycle wheel like a giant gyroscope to explore angular momentum and torque. Learners can participate in the assembly of the Bicycle Wheel Gyro or use a preassembled unit to explore these concepts and go for an unexpected spin!

This lesson begins with a demonstration prompting students to consider how current generates a magnetic field and the direction of the field that is generated. Through formal lecture, students learn Biot-Savart's law in order to calculate, most simply, the magnetic field produced in the center of a circular current carrying loop. For applications, students find it is necessary to integrate the field produced over all small segments in an actual current carrying wire.

Students make a skydiver and parachute contraption to demonstrate how drag caused by air resistance slows the descent of skydivers as they travel back to Earth. Gravity pulls the skydiver toward the Earth, while the air trapped by the parachute provides an upward resisting force (drag) on the skydiver.

This activity provides instructions for using a flashlight and aquarium (or other container of water) to explain why the sky is blue and sunsets are red. When the white light from the sun shines through the earth's atmosphere, it collides with gas molecules with the blue light scattering more than the other colors, leaving a dominant yellow-orange hue to the transmitted light. The scattered light makes the sky blue; the transmitted light makes the sunset reddish orange. The section entitled What's Going On? explains this phenomena.

Students learn how engineers gather data and model motion using vectors. They learn about using motion-tracking tools to observe, record, and analyze vectors associated with the motion of their own bodies. They do this qualitatively and quantitatively by analyzing several examples of their own body motion. As a final presentation, student teams act as engineering consultants and propose the use of (free) ARK Mirror technology to help sports teams evaluate body mechanics. A pre/post quiz is provided.

Calculating electron energy for levels n=1 to 3. Drawing a shell model diagram and an energy diagram for hydrogen, and then using the diagrams to calculate the energy required to excite an electron between different energy levels. Created by Jay.

Using classical physics to calculate the energy of electrons in Bohr model. Solving for energy of ground state and more generally for level n. Created by Jay

Using equation for Bohr model radii to draw shell model for n=1 to 3, and calculating the velocity of a ground state electron. Created by Jay

Using classical physics and vectors, plus assumption that angular momentum of electron is quantized, to derive the equation for Bohr model radii. Created by Jay.

Students revisit the mathematics required to find bone mineral density, to which they were introduced in lesson 2 of this unit. They learn the equation to find intensity, Beer's law, and how to use it. Then they complete a sheet of practice problems that use the equation.

Students examine an image produced by a cabinet x-ray system to determine if it is a quality bone mineral density image. They write in their journals about what they need to know to be able to make this judgment. Students learn about what bone mineral density is, how a BMD image can be obtained, and how it is related to the x-ray field. Students examine the process used to obtain a BMD image and how this process is related to mathematics, primarily through logarithmic functions. They study the relationship between logarithms and exponents, the properties of logarithms, common and natural logarithms, solving exponential equations and Beer's law.

In this optics activity, learners examine how polarized light can reveal stress patterns in clear plastic. Learners place a fork between two pieces of polarizing material and induce stress by squeezing the tines together. Learners will observe the colored stress pattern in the image of the plastic that is projected onto a screen using an overhead projector. Learners rotate one of the polarizing filters to explore which orientations give the most dramatic color effects. This activity can be related to bones, as bones develop stress patterns from the loads imposed upon them every day.

Experiment with rocket designs and a PVC launcher to discover how high—and how far—you can make your rockets go.